Friday, March 28, 2008

Upping the anti (depressant)

A paper on antidepressants by Kirsch and co-authors published last month in PLoS Medicine has received a lot of attention. The antidepressants studied are the six most widely prescribed approved between 1987 and 1999: Prozac, Paxil, Effexor, Serzone, Zoloft, and Celexa.

The Editors' Summary explains:
The researchers obtained data on all the clinical trials submitted to the FDA ... They then used meta-analytic techniques to investigate whether the initial severity of depression affected the HRSD [Hamilton Rating Scale for Depression] improvement scores for the drug and placebo groups in these trials. They confirmed first that the overall effect of these new generation of antidepressants was below the recommended criteria for clinical significance. Then they showed that there was virtually no difference in the improvement scores for drug and placebo in patients with moderate depression and only a small and clinically insignificant difference among patients with very severe depression. The difference in improvement between the antidepressant and placebo reached clinical significance, however, in patients with initial HRSD scores of more than 28—that is, in the most severely depressed patients. Additional analyses indicated that the apparent clinical effectiveness of the antidepressants among these most severely depressed patients reflected a decreased responsiveness to placebo rather than an increased responsiveness to antidepressants.
The press simplified it further. The MSNBC headline was "Antidepressants may not help many patients". The Guardian announced: "Prozac, used by 40m people, does not work say scientists".

Reactions, adverse and otherwise

There were reactions to the effect that "we've know all along antidepressants don't work" and at the other extreme "nothing could ever convince me that antidepressants don't work."

A lot of reaction came from people who believe they have benefited from antidepressants. See, for example, the comments following a summary of the study at

The blogosphere had plenty of reactions: FuturePundit, Action Potential (the Nature Neuroscience blog), The MindFields College Blog, and on and on.

And the journal itself, PLoS Medicine, had an enormous number of responses to the paper.

Betta check the meta

The heart of the findings in this paper is the meta-analysis itself, and when I examined it, two things jumped out immediately. The figure below shows them both.
There's a lot to look at in the figure. The red triangles represent the results of the patients who received the antidepressant. The bigger the triangles, the more weight they receive in the analysis. Similarly, the circles represent the placebo results. The solid red curve is a model fit to the antidepressant results. The dashed blue curve is a model fit to the placebo results. The green region shows where there is a clinically important difference between the curves.

First, look at the vertical axis, labeled "Improvement (d)" and ranging from 0 to 2. This is the mean improvement in the Hamilton Rating Scale for Depression (HRSD), but it has been divided by the standard deviation. Why divide it by the standard deviation? Well this is what you might do if each study was using a different rating scale, in order to standardize things. But here it's not necessary. Each study used the HRSD, so it would be better not to standardize.

Second, if triangles represent antidepressant results and circles represent placebo results from the studies, how do they pair up? Each study has two "arms": an antidepressant arm and a placebo arm, but on the figure you can't tell which triangle belongs with which circle. This points to an important problem: the authors meta-analyzed the antidepressant arms separately from the placebo arms. But the studies were randomized controlled trials, which means that within each study the two arms are comparable. Ignoring this can introduce bias. The standard approach in meta-analysis is to compute a contrast between the two arms within each study, and then meta-analyze these contrasts.

But do either of these points make much of a difference? It turns out that they do. PJ Leonard took the trouble of rerunning the analyses using raw HRSD scores and the standard meta-analytic approach rather than the separate-arms analysis of Kirsch and co-authors, and obtained an effect about 50% larger than they did, and stronger evidence of clinical importance. Leonard also performed a regression analysis corresponding to the figure above.

Robert Waldmann has also done some interesting work on this.

Overcoming depression: there's no silver bullet

The evidence doesn't seem to support the notion that antidepressants "don't work". The overheated media response to this article was unfortunate. And that's a topic in itself.

Nonetheless, it seems that on average the effect of antidepressants is hardly overwhelming. So far there's no silver bullet for depression. Drugs can help, but so can other interventions. Including kindness and understanding.

Update: 11Apr2008 Thanks for a post on The Home for Wayward Statisticians, I found a couple more interesting links. One is by Mark Liberman on Language Log. The other is an editorial in Nature.

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Tuesday, March 18, 2008

My selection for the meme team

I've been tagged by Zeno at Halfway There, with the following blog meme:
The rules are as follows:
1) Link to the person who tagged you.
2) List 5 random/weird things about your favorite historical figure.
3) Tag 5 more people at the end of your blog and link to theirs.
4) Let the person know they have been tagged by leaving a note on their blog.
I don't usually buy into this stuff, but why not? So my selection is ...

Charles S. Peirce (1839 — 1914)

I've chosen him even though I don't really believe in the idea of a "favorite historical figure". But he is really interesting. Peirce was an American philosopher, mathematician, scientist, and humanist. He has been extremely influential, yet he remains somewhat obscure.

1. Peirce's name is pronounced "purse". (The family name was originally spelled Pers.)

2. My choice of Peirce was entirely pragmatic.

3. Peirce invented a conformal map projection: the quincuncial projection.
It also turns out the map tessellates the plane, i.e. you can seamlessly tile the plane with rotated copies of the map. (Tessellation is also sometimes used in quilting.)

4. Peirce was one of the founders of the field of semiotics, which is about signs and their interpretation. On that theme (ok, it's a bit indirect), here's a video about signs:

5. Peirce developed a graphical system for representing logic called existential graphs. In 1984, John F. Sowa built on Peirce's ideas and ideas from semantic networks in artificial intelligence to develop conceptual graphs.

The meme made me do it

So now I'm supposed to tag some more folks with this meme. I nonbindingly-respectfully-whattheheckfully tag:

Ray Deonandan at Deonandia
Dr. Free-Ride at Adventures in Ethics and Science
Antonella Pavese at
Dr. B at Bitch Ph.D.
Jim Bobby at Jim Bobby Sez

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Saturday, March 08, 2008

Al Gore defies the laws of probability

As if the huge success of An Inconvenient Truth followed by winning the Nobel Peace Prize wasn't enough, now Al Gore is defying the laws of probability! At least in terms of probable outcomes of the U.S. Democratic nomination and the presidential election itself.

Intrade, the leading commercial prediction market lets you bet on political outcomes. For example, "Barack Obama to win 2008 US Presidential Election" is currently trading at 47.5, meaning the market believes there's a 47.5% chance Obama will be the next president.

What's the probability that Al Gore will win the Democratic nomination? As I write this, the market believes it's 1.7%. Seems fair enough ...

... until you look at the probability that Al Gore will be the next president. Curiously, the market believes that's 2.1%. How could that be? Don't you have to win the nomination before you have a chance of becoming the president? (My 13-year-old daughter points out that perhaps Gore could run as an independent, but hey, we're Canadians, so this is a great mystery to us. So for now, let's leave this possibility aside.)

Let's do a few probability calculations (note that the vertical bar | means "given than"):
Prob(Gore pres.)
= Prob(Gore pres. & Gore nom.)
= Prob(Gore pres. | Gore nom.) * Prob(Gore nom.)
Prob(Gore pres. | Gore nom.)
= Prob(Gore pres.) / Prob(Gore nom.)
Prob(Gore pres. | Gore nom.)
= 2.1%/1.7% = 123.5%
Therefore, if Gore is nominated, the probability he'll be elected president is 123.5%!

Of course there's no such thing as a probability above 100%, which suggests that something is amiss. Perhaps there is a belief that Gore might run as an independent, which would invalidate my assumption that he would have to win the Democratic nomination in order to become president. Or perhaps at any given time the prediction market isn't strictly coherent in the Bayesian sense that it should be consistent with the axioms of probability.

My interpretation is that Gore remains sufficiently attractive as a presidential candidate that if he were nominated, the chances of him winning the election are very high. But not quite 124%.

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Friday, March 07, 2008

Quilt complex

The quilt on the left is a Broken Star Variation. As Escher knew so well, there's no such thing as plain geometry. However it's possible to take this too far (ok, I don't really mean that!) Here are some amazing mathematical quilts by Diana Venters and Elaine Ellison, who have written a book, Mathematical Quilts: No Sewing Required.

Well, now it's time for me to quilt while I'm ahead. (I'll let you know how it turns out...)

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Thursday, March 06, 2008

Dragging the people along

As I pointed out in my recent post, democracy is not so easy to measure. The sine qua non of democracy is generally felt to be "free and fair elections". But that begs quite a few questions: Can you have "free and fair" elections without freedom of the press? How was the list of candidates assembled? Is wealth a precondition for running? Have there been any implicit or explicit threats conditional on the outcome?

But there's a lot more to democracy that elections ("free and fair" or otherwise). Elected representatives should be responsive to their constituents' concerns. When those concerns are consistently ignored, there is clearly a problem.

This has been just the case with Canadian public opinion on the war in Afghanistan. According to public opinion polling conducted by The Strategic Counsel for The Globe and Mail and CTV News, since the summer of 2006, a majority of Canadians have opposed sending troops to Afghanistan. In the poll of January 10th-13th, 47% said they would like to see Canadian troops return as soon as possible, 31% said the troops should remain in Afghanistan but hand over their combat role to another NATO country, and just 17% said that they should continue their combat role against the Taliban.
Of course the people don't want war. But after all, it's the leaders of the country who determine the policy, and it's always a simple matter to drag the people along whether it's a democracy, a fascist dictatorship, or a parliament, or a communist dictatorship. Voice or no voice, the people can always be brought to the bidding of the leaders. That is easy. All you have to do is tell them they are being attacked, and denounce the pacifists for lack of patriotism, and exposing the country to greater danger.
                                   — Hermann Göring
These words are chilling, not just because they were uttered by one of the top Nazis, but because they continue to be put into practice.

What're we fightin' for?

According to the government:
Our goal is to protect Canadians by ensuring that Afghanistan never again falls into the hands of the Taliban and that Afghanistan becomes a stable, free and democratic society.
Interestingly, despite the grandiose language, the supposed danger is only hinted at.

To boost support for the war, it helps to fan the flames of patriotism. And what better way than banners and decals proclaiming "We support our troops!" In several cities across Canada, including Ottawa and Toronto (where there was considerable controversy), decals have been put on police cars and fire engines.

Proponents claim that there's nothing wrong with this, that it's just expressing concern for the wellbeing of Canadian troops. But as many have pointed out, there's a political message here and dissent is being marginalized. It seems to me that putting political messages on public vehicles damages democracy.

To further stifle debate, here's General Rick Hillier, Canada's Chief of Defense Staff:
I'm not going to stand here and tell you that the suicide bombings of this past week have been related to the debate back here in Canada. But I also cannot stand here and say that they are not.
Imposing democracy

The great irony is that these anti-democratic developments are justified as advancing the cause of democracy in Afghanistan. But as Ghandi said:
The spirit of democracy cannot be imposed from without. It has to come from within.

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Tuesday, March 04, 2008

Is it fair not to share?

Over at Adventures in Ethics and Science there's a very interesting post and follow-up comments on whether researchers should share data. It's based on a recent New York Times article by biostatistician Andrew Vickers (Cancer Data? Sorry, can't have it).

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Monday, March 03, 2008

Paint by numbers

The map on the left labels countries as free (green), partly free (peach), and not free (red) for the year 2006. The classification is from Freedom House, a primarily US-government-funded organization. Each country is scored on political liberty and civil liberty; the combined average of these scores determines how the country is classified. Cuba, for example, receives the poorest rating on both political and civil liberties, and is thus categorized as "not free".

The Wikipedia entry for democracy lists two other measures of democracy, one from the Polity IV project and the Democracy Index from The Economist. Each measure has its own scheme for measuring and weighting different characteristics felt to characterize democracies. Since the different measures assess many of the same things, it is not surprising that they show some agreement.

But democracy is not a simple thing and it is far from clear which characteristics matter and how best to weight them. For example, does a free press count more than an independent judiciary? If so, by how much? (And presumably this depends on how "free" and how "independent" they are.) What about non-traditional characteristics that may be important measures of democracy? For example, should voter turnout be factored in? What about incarceration rate? Or media concentration? Or universal health care?

Although there may be some value in overall measures of democracy, individual characteristics still need to be examined and put in context. When we do that, we may find that the global canvas no longer looks like a paint by numbers kit.

Update: 05Mar2008

No sooner had I put up this post than I saw this Adbusters press release relating to media concentration and democracy:

Adbusters Demands Canwest, the CBC and the CRTC Stop Blocking Citizen-Produced Advertising

On Monday, February 18, Adbusters lost its court battle against two of Canada's television networks that refused to sell airtime for its commercials. Adbusters claimed the CBC and Canwest Global had violated its right to free speech under the Canadian Charter of Rights and Freedoms by refusing to sell air time, but the court decided that the Charter does not apply to private corporations.

"It's outrageous that the fast food, oil and automobile industries can buy as much TV time as they want in order to promote their agendas, but citizens are not allowed to talk back," said Adbusters Editor-in-Chief Kalle Lasn in response to the ruling. "Canadian democracy will not work properly until we the people have the same right to buy airtime as corporations do."

The rejected Adbusters ads pointed out that over 50 percent of the calories in a Big Mac come from fat, called for an end to the age of the automobile, and promoted Buy Nothing Day. While Court Justice William Ehrcke ruled that private broadcasters have the right to run whatever ads they like, Adbusters feels the case raises some troubling questions.

Firstly, why are Canwest and the CBC selling as much time as they possibly can to corporations, while fighting expensive legal actions to keep citizen-produced messages off the air? Why does the CBC call itself "Canada's Public Broadcaster" if they won't sell airtime to citizens?

Secondly, why is the CRTC not standing up for public access? When they grant licences to broadcasters, why is the right of Canadian citizens to access their own "public" airwaves not being guaranteed? Thirdly, why is our freedom of speech being suppressed? Why can corporations buy airtime while citizens cannot? Why doesn't the Canadian Charter apply to the most powerful social communications medium of our age - television?

"This case goes to the very heart of what our democracy is all about," says Lasn. "A healthy society allows its citizens to walk into their local TV stations and buy airtime under the same rules and conditions that corporations do. Adbusters has been given 30 days to challenge the ruling. This legal battle for media democracy will go on."

To talk to Kalle Lasn, or Ryan Dalziel, our lawyer, about the case please contact Lauren Bercovitch (


For more information about Adbusters and the global media democracy movement visit and

[1] Canadian Media facts:

Three corporations (CanWest, Quebecor and Torstar) control 70 per cent of the country's daily newspaper circulation.

Five major media acquisitions in Canada have been approved by CRTC in the past year: CHUM was purchased by CTVglobemedia for $1.4 billion, which then sold five CityTV stations to Rogers Communications for $375 million; CanWest purchased Alliance Atlantis for $2.3 billion; Astral Media bought Standard Broadcasting for $1.2 billion; and Quebecor bought the Osprey Media newspaper chain for $414 million.

[2] Facts about Media Democracy:

More than 30,000 people have signed the Media Carta, to voice their concerns about the way information is distributed in our society.

In the past year, a growing number of grassroots media activist groups have been formed in Canada to express a dissatisfaction with the continued consolidation of the country's media:

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